From: "Dirk Van de moortel" Subject: Re: Lion and Christian (Was:Hunter and deer) Date: Wed, 31 Jan 2001 17:22:58 GMT Newsgroups: sci.math Summary: Pursuit problems (Besicovich's optimal strategy for the Christian) "Virgil" wrote in message news:Vmhjr-8475CA.13092030012001@news.frii.com... > In article <955rs7$fr3$1@nnrp1.deja.com>, Ron Larham > wrote: > > > > You didn't say that the lion is a dumb chaser, i.e. that he can > > > anticipate where the christian is going next. I'll assume that the > > > lion is less intelligent than that Neandertal guy. > > The ultimate solution is valid if both the lion and the man are Mensa > members, or even 4-sigma members. No limit is imposed on the > intelligence of the loser. The winner need only know his/its best > strategy and be able to impliment it. > > It was discovered by A. S. Besicovitch, and first published in 1953, but > not by Besicovitch. Guess what.... I was curious about this Besicovitch and did a google search. Abd behold, after a while I found this site: http://www.amsta.leeds.ac.uk/pure/staff/partington/personal/quintics.html An extract: | A few more curious games to conclude with, that have no connexion | with the above. | First, The Lion and the Christian. The lion, L, and the Christian, | C, are in a circular arena (unit radius), and L is chasing C with | the object of eating him. Both move at unit speed, and are | conveniently regarded as points. If L is at the centre, and C | stays on the circumference, then it is not hard to show that L | catches C in a time of pi/2, travelling on a pursuit curve. | However C can do better (as Besicovitch showed). He moves towards | L to start with, then makes a sequence of zig-zag steps at right | angles to the direction the lion is from him at the start of each | step: if the step lengths are chosen to be (di), where the sum of | the (di) is infinite (so he is travelling for infinite time) and | the sum of the (di2) is small and finite (so that he doesn't end | up on the circumference again), C can evade L indefinitely. So it IS possible :-) Dirk Vdm